CRPJAC Statement :: SAS/OR(R) 12.1 User's Guide: Mathematical Programming Legacy Procedures

CRPJAC Statement

CRPJAC variables ;

The CRPJAC statement defines the crossproduct Jacobian matrix used in solving least squares problems. For more information, see the section Derivatives. If the DIAHES option is not specified, the CRPJAC statement lists variable names, which correspond to the elements $(J^ T J)_{j,k},\ j \geq k$ of the lower triangle of the symmetric crossproduct Jacobian matrix listed by rows. For example, the statements

   lsq f1-f3;
   decvar x1-x3;
   crpjac jj1-jj6;

correspond to the crossproduct Jacobian matrix

$J^ TJ = \left[ \begin{array}{ccc} JJ1 & JJ2 & JJ4 \\ JJ2 & JJ3 & JJ5 \\ JJ4 & JJ5 & JJ6 \\ \end{array} \right]$

If the DIAHES option is specified, only the diagonal elements must be listed in the CRPJAC statement. The rows and columns of the crossproduct Jacobian matrix must be in the same order as the corresponding parameter names listed in the DECVAR statement. To specify the values of nonzero derivatives, the variables specified in the CRPJAC statement have to be defined at the left-hand side of algebraic expressions in programming statements. For example, consider the Rosenbrock function:

proc nlp tech=levmar;
   lsq f1 f2;
   decvar x1 x2;
   gradient g1 g2;
   crpjac cpj1-cpj3;
   
   f1   = 10 * (x2 - x1 * x1);
   f2   = 1 - x1;
   g1   = -200 * x1 * (x2 - x1 * x1) - (1 - x1);
   g2   =  100 * (x2 - x1 * x1);
   
   cpj1 = 400 * x1 * x1 + 1 ;
   cpj2 = -200 * x1;
   cpj3 = 100;
run;